Jeremy Gormly, counsel assisting the New South Wales state coroner, said the 38-year-old was hit by six fragments of a police bullet, or bullets, with one striking a major blood vessel.

"She lost consciousness quickly and died shortly afterwards," Gormly said at the opening of the inquest.

The cafe manager's execution was witnessed by a police marksman, Gormly said.

Monis, 50, who fired five rounds from a sawn-off pump action shotgun, was killed instantly by several police bullets and bullet fragments to the head and body, Gormly added.

The inquest is running alongside a government inquiry into how Monis was able to access a gun and why he was granted bail while facing charges as an accessory to the murder of his ex-wife. He was also facing more than 40 sexual assault charges.

Dramatic: Two hostages run for cover behind a policeman during a hostage siege in Sydney (Photo: Getty Images)

The self-styled sheik harboured deep grievances against the Australian government and had found little kinship in the city’s large Muslim community, where he was seen as deeply troubled.

He was found guilty in 2012 of sending threatening letters to the families of eight Australian soldiers killed in Afghanistan as a protest against Australia’s involvement there.

Gormly said investigators had so far not established any contact between Monis and Islamic State before the siege.

There was evidence that a psychiatric profile of Monis "will throw light" on his motivations, he said.

Monis ordered and consumed a piece of chocolate cake and tea after entering the cafe, the inquest heard.